Barclays PLC Chairman John McFarlane on Wednesday defended the bank's chief executive, Jes Staley, as several shareholders called for the U.S. banker to be fired over his role in trying to unmask a whistleblower.

Mr. Staley faced criticism after U.K. regulators launched a probe over his repeated attempts to try to reveal the identity of a whistleblower who sent letters criticizing a hire he made. At the bank's annual general meeting a couple of shareholders called for Mr. Staley to be replaced. "Has the behavior of the chief executive brought nothing but shame on the name of Barcays?" asked one shareholder.

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Mr. McFarlane said he stood behind Mr. Staley. "You know me. If I believe he should go, you know he would go," said Mr. McFarlane, who is dubbed "Mack the Knife" because of his track record in axing top executives. He said Mr. Staley had "gone through a red light" and "when you go through a red light you don't lose your license."

Mr. Staley had made a mistake and wasn't planning to do anything malicious to the whistleblower, he said. "All he wanted to do was phone them up and ask them to stop sending the letters," he said. The Barclays board has reprimanded Mr. Staley and said it would dock a chunk of his bonus after the regulators' probe finishes.

Separately, Barclays agreed to pay about $97 million in a settlement after allegedly overbilling clients, the U.S. Securities and Exchange Commission said Wednesday.

Mr. Staley took an additional hit last month after The Wall Street Journal reported he became embroiled in a battle with KKR & Co., a major client of the bank, after backing his brother-in-law who is locked in a dispute with the private-equity giant. KKR has recently cut Barclays off from some of its business as a result of the executive's interventions, according to people familiar with the matter. On Wednesday, Mr. McFarlane defended this action too, saying Mr. Staley "didn't actually do anything. He did consult but we advised him not to do anything."

Some 97% of the shareholders who voted backed Mr. Staley's reappointment on Wednesday, but 16% of shareholders either abstained or voted against the CEO following a recommendation to abstain by a proxy adviser.

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One major investor said it is in "wait and see" mode ahead of the whistleblowing probes' conclusions. The Barclays board, meanwhile, has endorsed Mr. Staley over both matters and hopes the current concerns will subside by the time the regulators' investigations are finished, a process that could take up to a year, according to one person familiar with the board's thinking.

Barclays is on its fourth leader in five years. So far investors have broadly welcomed Mr. Staley's strategy of backing the Barclays investment-banking franchise while shedding numerous businesses around the globe. But returns remain tepid. Next month Barclays is expected to announce the closure of its "noncore" division, which houses assets the bank wants to ditch. Even as this milestone approaches investors are turning to other worries, namely that the bank's capital base is too thin.

Barclays is locked in a legal battle with the U.S. Justice Department over its role in the sale of toxic mortgage-backed securities. It also has to drum up extra capital to pump into its U.S. unit to ensure it can pass stress tests. A plan to sell down its African business is still waiting on regulatory signoff in South Africa. Analysts at Goldman Sachs last week expressed worries that Barclays is undercapitalized compared with European peers but played down the idea the bank would have to tap shareholders for cash. "We believe an external capital raise is low on the list of capital build options," analysts at Goldman Sachs wrote in a recent note.

Mr. Staley said the bank "still has a lot more work to do," especially in upgrading its investment bank.

On Wednesday, the SEC said Barclays improperly recommended more expensive share classes, charged fees to clients for due diligence and monitoring services that weren't performed and collected extra mutual-fund sales charges and fees. Some clients also allegedly paid excess fees to Barclays due to miscalculations and billing errors. Much of the alleged behavior occurred between 2010 and 2015.

As part of the settlement, Barclays didn't admit or deny guilt. A Barclays spokesman declined to comment further.

In 2015, Barclays agreed to sell its U.S. wealth and investment management unit to Stifel Financial Corp.

Barclays will pay back $49.8 million, $13.8 million in interest, $3.5 million to advisory clients and a $30 million penalty.